Subsidizing research programs with “if” and “when” uncertainty in the face of severe informational constraints

• Date: 01 June 2018
• DOI: http://doi.org/10.1111/1756-2171.12227
• Published date: 01 June 2018
• Author: Jian Tong,Jason Jianjun Wu,David Besanko

RAND Journal of Economics

Vol.49, No. 2, Summer 2018

pp. 285–310

Subsidizing research programs with “if” and

“when” uncertainty in the face of severe

informational constraints

David Besanko∗

Jian Tong∗∗

and

Jason Jianjun Wu∗∗∗

We study subsidy policies for research programs when firms have private information about the

likelihood of project viability,but the government cannot form a unique prior about this likelihood.

When the shadow cost of public funds is zero, first-best welfare can be attained as a (belief-free)

ex post equilibrium under both monopoly and competition, but it cannot be attained when the

shadow cost is positive. However, max-min subsidy policies exist under monopoly and competition

and consist of pure matching subsidies. Under a Research and Development (R&D) consortium,

the highest max-min matching rateis lower than under competition, and R&D investment intensity

is higher.

1. Introduction

Governments have long played a role in subsidizing private investments in R&D. The

principal economic justification for R&D subsidies is the presence of market imperfections (e.g.,

limits on appropriability or problems of free-riding) that result in socially suboptimal provision

of private R&D (Arrow, 1962). However, the economic literature presents mixed results on how

effectively subsidies can address these market failures. Some empirical studies conclude that

R&D subsidies stimulate private R&D investment (e.g., Lach, 2002; Almus and Czarnitzki,

2003), whereas others find that subsidies crowd out private R&D investment (e.g., Irwin and

Klenow, 1996; Wallsten, 2000) or leave it unchanged (e.g., Klette and Moen, 1999, 2012). The

∗Northwestern University; d-besanko@kellogg.northwestern.edu.

∗∗University of Southampton; j.tong@soton.ac.uk.

∗∗∗Compass Lexecon; jwu@compasslexecon.com.

The authors would like to thank Alberto Galasso and Nick Klein for their very helpful comments as well as participants

at 2009 International Industrial Organization Conference at Boston and 2010 Southwest Economic Theory Conference

at Los Angeles. We also thank Mark Armstrong and two anonymousreferees for their extremely conscientious reviews

and for their valuable suggestions. Besanko gratefully acknowledges the financial support from the National Science

Foundation under grant no. 0615615.

C2018, The RAND Corporation. 285

286 / THE RAND JOURNAL OF ECONOMICS

theoretical literature (discussed in more detail below) shows that subsidies can, in principle,

stimulate private R&D investmentand increase social welfare, but the models in the literature are

typically cast within static and/or deterministic settings that seem far removed from the dynamic

and uncertain environments in which much modern research (especially basic research) takes

place. From both a theoretical and empirical perspective, the effectiveness of government R&D

subsidies remains an unsettled question, and as Hall (2005) suggests, it deserves further research.

The purpose of this article is to advance the theory of R&D subsidies by studying their impact

in a setting with two key features: (i) firms undertake a research program that involvesuncertainty

about the timing of the scientific breakthrough that the program can lead to (“when uncertainty”)

and about the underlying viability of the program (“if uncertainty”); (ii) firms’ prior beliefs about

program viability are private information, and the government providing the subsidies is unable

to form a unique prior belief about the firms’ priors. That is, the subsidizing government faces a

severe informational asymmetry—it neither knows how optimistic firms are about the viability

of the research program, nor does it know what to believe about firms’ optimism. These features

seem especially likely to hold for research programs taking place in “uncharted waters,” so our

theory is particularly relevant for groundbreaking research programs in areas in which there is

little established consensus about whether the current direction of inquiry is likely to be fruitful.

This article makes two contributions. First, weshow that the way in which R&D is subsidized

matters. Certain types of subsidies (i.e., earmarked funding in which a firm is required to spend

a certain minimum amount on the project) may suppress private investment,whereas other types

of subsidies (i.e., a pure matching subsidy in which a firm undertaking R&D is reimbursed a

fraction of its R&D expenses) may stimulate private investment. This suggests that empirical

studies of how subsidies impact private R&D investment need to be cognizant of how subsidies

are structured. Second, we show that despite the government’s severe informational constraints,

a simple mechanism—in particular, a pure matching subsidy—can still perform reasonably well

with respect to plausible decision criteria, and under interesting circumstances, it can even attain

the first-best level of welfare.

More specifically, this article uses a two-armed bandit model of R&D investment in which

firms seek to achieve a scientific breakthrough.1As time passes and the breakthrough is not

achieved, the firms’ posterior probability that the project is viable falls. In the absence of a sub-

sidy, once that posterior reaches an abandonment threshold—which depends on the payoff from

achieving the breakthrough, the marginal cost of R&D investment, and the rate at which invest-

ment increases the likelihood of a viable project achieving a breakthrough—firms stop investing

and terminate the project. To incentivize private R&D investment, the government provides firms

with an R&D subsidy that depends on their R&D investments. The subsidy mechanism that we

consider subsumes three specific funding schemes commonly used in practice: a pure matching

subsidy, an earmarked subsidy, and an unrestricted subsidy, in which the government makes

an open-ended commitment to fund the project until a breakthrough occurs (though unlike an

earmarked subsidy, there is no formal requirement that the firm actually spend the money on the

focal R&D project).

We consider two cases: monopoly R&D, in which the breakthrough is pursued by a single

firm, and R&D competition, in which N>1 firms compete to achieve the breakthrough. Under

monopoly R&D, the matching component of the subsidy reduces the abandonment threshold,

thus expanding the range of posterior beliefs over whichthe monopolist under takes the maximum

feasible R&D investment, whereas the earmarked and unrestricted components of the subsidy

increase the abandonment threshold, shrinking the range of maximum investment. Under R&D

competition, a complication arises that does not exist under monopoly: the possibility that firms

may free-ride on the R&D efforts of other firms. In this setting, the unrestricted component to the

1The use of two-armed bandit models in economics dates back to Rothschild (1974). Keller, Rady, and Cripps

(2005) and Klein and Rady (2011) focus on the strategic interaction among agents in a bandit framework. The model in

this article is closest to Keller, Rady,and Cripps (2005).

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